Differentiated Problem Share Out - Unit Review

Objective

This lesson is designed to allow the students share out their findings connected to the applications of logarithmic and exponential functions problems. The 5 different problems that have been previously rolled-out each provide a unique challenge for the students. Today is when the students get to take center stage of their group and showcase their results and strategies!

Big Idea

This lesson allows the students to apply their mathematical knowledge in a real context.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Problem Wrap-Up

15 minutes

As the students enter, instruct them to sit with their partners from the previous day’s investigation.

To set the tone for the start of class, I pull up an online timer on my projector screen and display 15 minutes. http://timer.onlineclock.net/ With this displayed, the students hardly need any pep-talk to get themselves going! Typically most of the groups already have, or are approaching, their solutions. The students usually use this time to organize their work and prepare with their partner for the share-out session. As the self-sufficient groups wrap things up, I focus on the group or two that is struggling through the problem. It is important to emphasize that wrong answers and wrong approaches are GREAT in this activity! Although we desire the correct answer, allowing the students the latitude to present failed attempts at solving the problem is equally important. I make a big deal in front of the class about the groups who persevere through the problem, and learn from failed attempts. Students need commended for stepping up and talking about dead ends and mathematically incorrect attempts at a solution! This creates an awesome classroom culture! As I rotate the room during these 15 minutes, I work hard to convey this message to the group or two that is frustrated because they have not found the correct solution. I tell them that they still have SO MUCH to share out!

Online Timer

Differentiated Problem Set Problem #1-2.pdf

Differentiated Problem Set Problem #3-4.pdf

Differentiated Problem Set Problem #5.pdf

Share Out

25 minutes

Once the timer has expired, it is time to group the students into larger groups of 4-5 pairs (8-10 students total). In my classroom, it only takes me about 60 seconds to move the desks around to accommodate a discussion setting. I have even purchased whiteboard easels for my classroom and days like this – they are well worth the money, and you can even write a grant for them!

Prior to class, I have pre-determined the share out groups. This ensures a smooth transition between work time and share out. A few key elements about the share out and group structure:

1) Group pairs together who have different problems. No group should have students in it who attempted the exact same problem as themselves.

-Keeping a list of what students are attempting a particular problem is quite helpful

2) Display the stop watch on the projector screen

-5 minutes per group MAX – continue to reset the timer after each 5 minute session

Allows them to summarize their Know’s/N2K’s, talk about their process, and list any other key details they discovered

What challenges and difficulties did you face?

Allow the “audience” to interact and ask questions at any time!

3) Teacher Behavior and Grading

-Keep a journal log of key conversations to bring up for debrief at the end of class

Debrief

10 minutes

The conclusion of the lesson is all about giving shout-out’s and emphasizing classroom culture! Too many times in math class this important debrief time is scratched or overlooked. After an intense mathematical investigation it is very rewarding and worthwhile to take a few extra minutes to celebrate successes – not just correct answers! As you debrief with students, do not be afraid to open it up to them. I commonly as my students what they enjoyed about the activity, and what they would do differently for next time. All in all, my students really loved this activity and especially liked seeing a wide variety of problems! They felt that the time limits that I gave them were sufficient to brainstorm about the problem and they said that they enjoyed how I valued “problem solving process” over just getting the correct answer. The students especially seemed to like the “Seismologist” and “Chef’s Delight” problems because they provided them with the opportunity to research and compare their own earthquakes/foods. One group even made no-bake-cookies to illustrate Newton’s Law of Cooling! They even had a data chart of temperatures they had taken – IT WAS OUTSTANDING to see them motivated to do this all on their own time!

Please Note: As class concludes, remember to mention to the students what was talked about in the Strategies Folder video. As a teacher, it would be impossible for you to catch every second of every conversation during the share-out time. Tell the students that if they feel the grade that they receive is inaccurate, then they can schedule a time to come in and demonstrate their knowledge. My kids love (and understand) why I do this!

Whole Group Share-Out Protocol.MOV

Circulate Test Review Sheet

2 minutes

The end of the unit has arrived! I circulate the test review sheet at the end of class (if I have not done so already) so that the students have a day to look over it prior to asking questions in class.